After ours was installed I stumbled across a company that makes an all in one unit called Eternal Hybrid (link below). You may want to contact them and see about getting the energy efficiency specs to go that route. I think Navien also makes an all in one system now too. I would think either company would be able to give you more accurate energy specs and better answer your question. The other thing to keep in mind is that without the loop (& pump), you are in effect wasting gallons of water waiting for the hot to kick in--think showers, sinks, etc. How much does the water wastage cost in terms of both water & sewer bills + the unnecessary waste of a resource? In addition to washing machines not pulling enough water through at a time to trigger the heater and then remain on long enough to actually get the water down the line to the machine, some dishwashers are having problems too. Here is a link that might be useful: Eternal Hybrid Hot Water Heater Site

The re-set button on electric water heaters is typically a separate part of the upper thermostat block that functions as a high limit cut-off by using a bi-metal disc ("Snap-Disc") to interrupt power. The disc can fatigue, though rarely. The back of its housing should be in contact with the tank. The elements themselves should have no voltage leaking to ground (tank). Test that first. If unfamiliar to you, or lacking a tester, hire an electrician. I will assume you have set the thermostats to a reasonable level and verified output water temp. with a thermometer, that the heater itself is not in a high ambient temperature location, and that all wiring connections are tight.

What he said^^^^^^^,you must continue holding the button down for time stated next to button. If it still gos out,make sure the flame is touching tip of thermocouple. Thermocouple is a wire 3 times diamiter of a round tooth pick leading from near the button to piolet liight. If flame is touching,thermocouple has likly burnt out. Very common. It is inexpensive,available at most hardware stores and can be replaced by average home handyman.

You did already check the reset button on the WH thermostat, didn't you? Replacing WH elements is an easy DIY job. Whether it's worth it depends on the age and general condition of the WH, though the elements run only less than $20 each (there are two). It's less likely, but you also may need to replace the thermostat. Don't neglect to flush the WH via the bottom drain valve.